Electrical musical instruments of the voltage-controlled synthesizer type generally modify the spectral envelope of a complex tone signal compounded from one or more oscillator outputs by passing the signal through one or more fixed or variable filters. Control of spectral envelope is an essential ingredient in the definition of musical timbres, and virtually all listeners prefer musical sounds with time-varying timbre over "dead" sound without variation. For example, the frequency variations which musicians call "vibrato" are time-varying timbral effects.
Voltage-controlled filters are almost universally employed for more complex spectral manipulations. Such filters may be of the low-, high-, or band-pass type, with the bandwidth dependent on an externally provided control voltage. Processing signals with such variable-bandwidth filters are called subtractive synthesis, and a variety of patents have been issued on musical instruments which make use of subtractive synthesis, e.g., Robert A. Moog, Electronic Music Synthesizer, U.S. Pat. No. 4,050,343.
Criticism has been directed at the inability of musical synthesizers, of the type well-known in the art, to generate "natural" sounds. An alternative method based on audio frequency modulation and implementation by a digital FM synthesizer has been developed recently by J. W. Chowning, Method of Synthesizing a Musical Sound, U.S. Pat. No. 4,018,121.
The Chowning digital FM Synthesizer uses several dozen digital integrated circuits to form a micro-programmed device with "a sine memory which is a read only memory." The basic purpose of the micro-program is to cyclically obtain values from the sine table stored in the sine memory and combine them with appropriate input values of carrier frequency w.sub.c, modulation frequency w.sub.m, modulation index I and amplitude A to calculate in real-time instantaneous output values of the form: EQU e=A sin (w.sub.c t+I(t) sin w.sub.m t). (FM Equation)
The key time-varying parameter is the modulation index I(t) which gives "life" to the calculated signal e through the course of a note. It is shown in standard texts, e.g., Mischa Schwartz, Information Transmission, Modulation, and Noise, A Unified Approach to Communication Systems, Second Edition, McGraw-Hill Book Company, 1970, that the bandwidth of e is directly proportional to the modulation index I (page 246). This is a direct consequence of the mathematics of taking the sine of a sine in the FM EQUATION.
While the digital FM synthesizer is preferred by some as more "natural" sounding for musical purposes than the voltage-controlled subtractive synthesizers, there are inherent disadvantages to the digital FM synthesizer. First, as a digital device it is not easily connected to analog synthesizers, and requires digital to analog converter apparatus for musicians seeking to take advantage of both technical realms. Second, the digital FM synthesizer is elaborate and costly to manufacture, requiring a large number of integrated circuits. Third, it is restrictive in relying on sinusoids for synthesizing controlled-bandwidth signals.